Of the symbolic manipulation looking after the complexities. It
Seems likely that the theory of sets, especially as developed by
Bourbaki and Riguet, will provide the technique. But further
Research is needed into these questions.
Interference. If acid and alkali are passed along the same
Pipe they destroy each other; what will happen if two messages
Are passed along the same channel?— will they interfere with, and
Destroy, each other?
Simple examples are quite sufficient to establish that the same
Physical channel may well carry more than one message without
Interference, each message travelling as if the others did not exist.
Suppose, for instance, that a sender wanted to let a recipient know
Daily, by an advertisement in the personal column of a newspaper,
Which of 26 different events was being referred to, and suppose he
Arranged to print a single letter as the coded form. The same chan-
Nel of “one printed letter” could simultaneously be used to carry
Other messages, of variety two, by letting the letter be printed as
Lower case or capital. The two messages would then be transmit-
Ted with as little interference as if they were on separate pages.
Thus, if ten successive messages were sent, N K e S z t y Z w m
Would transmit both n k e s z t y z w m and 1 1 0 1 0 0 0 1 0 0
Completely. It is thus possible for two messages to pass through
The same physical thing without mutual destruction.
As an example of rather different type, consider the transforma-
tion of Ex. 2/14/11, and regard the position of, say, A''' as a coded
form of that of A (with B''' similarly as the coded form of B). Thus
Treasure might be buried at A and weapons at B, with recording
marks left at A''' and B'''. Now a change in the position of B leads
to a change of A''', so B’s value plays an essential part in the cod-
ing of A to A''' (and conversely of A on B'''); so the two messages
158
Interact. Nevertheless the interaction is not destructive to the
Information about where the treasure and the weapons are, for
given the positions of A"' and B"', those of A and B can always be
Reconstructed, i.e. the messages are still capable of being exactly
Decoded.
The conditions necessary that two messages should not inter-
|
|
|
Fere destructively can be found by considering the basic fact of
Coding— that a set of messages are converted to a set of trans-
Forms (S.8/4)— and by using the fact that any two messages of dif-
Ferent type can be laid side by side and considered as components
Of one “vector” message, just as any two variables can always be
Regarded as components of one vector. Thus if, in the example of
The printed letter, x represents the variable “which message of the
And y represents the variable “which of the two”, then the
Printed symbol is a coding of the single message (x,y).
Suppose it is given that the two messages x and y do not interfere
Destructively. This implies that both x’s and y’s values are recon-
Structible from the received form. It follows that if two primary
Messages are distinct, then their coded forms must be distinct (for
Otherwise unique decoding would not be possible). From this it fol-
Lows that, if the interaction is to be non-destructive, the variety in
The received forms must be not less than that in the original. This
Condition holds in the example of the printed letter, for both the
original messages and the printed form have variety of 26 × 2.
The fact that chaos does not necessarily occur when two mes-
Sages meet in the same channel is of great importance in
Neuro-physiology, especially in that of the cerebral cortex. Here
The richness of connexion is so great that much mixing of mes-
Sages must inevitably occur, if only from the lack of any method
For keeping them apart. Thus a stream of impulses coming from
The auditory cortex and carrying information relevant to one reac-
Tion may meet a stream of impulses coming from the visual cortex
Carrying information relevant to some other reaction. It has been
|
|
|
An outstanding problem in neurophysiology to know how destruc-
Tive interaction and chaos is avoided.
The discussion of this section has shown, however, that the
Problem is badly stated. Chaos does not necessarily occur when
Дата добавления: 2019-11-16; просмотров: 221; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!